A Torsion-Free Nonsofic Hyperbolic Group from Marked Lines

Candidate proof, not externally peer reviewed. The manuscript asserts the existence of a torsion-free nonsofic word-hyperbolic group with a finite two-dimensional classifying space carrying a locally CAT(-1) metric. The new ingredient is a quantitative rank obstruction for approximate permutation actions, uniform in the permutation degree. A separate five-dimensional incidence construction supplies the geometric data by a terminating finite search; the full presentation at the stated parameters has not been materialized. The marked-line construction, triangle wiring, interpolation identity, fixed-prime rank comparison, exceptional-set method, and exact finite-quotient rank obstruction are inherited from OpenAI family 252 and credited in the manuscript. Classical mathematical sources are also cited there. Disclosure: the mathematical derivation and manuscript were produced with substantial assistance from OpenAI language models. The human contact has not independently certified every argument. Released without a named mathematical author. The depositor serves as correspondence contact and makes no claim to personal mathematical authorship. Contact: harjas.sandhu@student.uq.edu.au. Corrections and adversarial scrutiny are welcome. Please identify the version, theorem, lemma or equation, and the disputed step. Independent mathematical development is welcome; preserve attribution to the inherited sources. The archived package contains the compiled PDF and standalone LaTeX source. This is manuscript version 1, first released on 7 October 2026. Read the PDF · Original version 1 release